Reich did not have a timetable for when his star running back might return.
Mack, who leads the Colts with 862 yards rushing and seven rushing touchdowns, injured his hand in the third quarter of Sunday's 33-13 victory over the Jacksonville Jaguars. It's uncertain how the injury occurred.
"I felt like pain in my hand," Mack said. "I didn't want to risk it anymore after that. It was crazy. I broke the last tackle and I got pushed out of bounds. Life is a balancing act. It's how you get back from it. Having to be patient with it."
The injury, a fracture of the metacarpal bone in Mack's right hand, is not thought to be season-ending at this time, sources tell ESPN's Adam Schefter.
"We'll miss Marlon, he is having a great year, but feel very confident in all three of those guys," Reich said.
Jonathan Williams and Jordan Wilkins, who missed Sunday's game against the Jaguars, will split Mack's carries until Mack returns, Reich said. Nyheim Hines will be the third-down back. Williams, who went into Sunday with just 1 yard rushing on the season, rushed for a career-high 116 yards against the Jaguars.
The Colts play their AFC South rival Houston Texans on Thursday night with the teams tied atop the division with 6-4 records.
Mack was having his best game since Week 5 at Kansas City before the injury, rushing 14 times for 109 yards, including four runs of at least 10 yards against the Jaguars.
Indianapolis rushed for 264 yards, its highest in 15 years against Jacksonville, and Williams and Mack are the first two Colts running backs to rush for at least 100 yards in the same game since Randy McMillan and Albert Bentley did it on Oct. 6, 1985.
"Everyone knows Marlon is having an incredible year," Reich said. "If you're going to lose him for however long you're going to lose him for, it's nice that we're coming off a game where Jonathan played the way he played. Everyone knows how much confidence we have in Jordan, and of course Nyheim. We all know what he can do. It's crazy to think you can lose a player of Marlon's caliber and feel you're going to miss him, but we're good. These guys behind are really good players."